Conditional Probability Calculator
Compute the conditional probability P(A|B) from the joint probability P(A∩B) and P(B), with an optional independence check.
Probability of A given that B occurred
45%
of BP(A∩B)
45%
B without A
55%
- 1
Conditioning event P(B)
P(B) = 0.4 = 0.4 - 2
P(A | B)
P(A∩B) ÷ P(B) = 0.18 ÷ 0.4 = 0.4500Conditional probability: what fraction of B outcomes also satisfy A.
How does this calculator work?
Conditional probability P(A|B) is the chance event A occurs given B already happened, computed as P(A∩B) divided by P(B). Enter the joint probability and P(B) to get P(A|B); add P(A) to also obtain P(B|A) and test whether the events are independent, which holds when P(A∩B) equals P(A) times P(B).
Formula
How this is calculated
Conditional probability measures how likely event A is once you know event B has already happened. You enter P(A∩B), the joint probability that both A and B occur, and P(B), the probability of the conditioning event. The calculator divides the joint probability by P(B) to give P(A|B) = P(A∩B) / P(B). All probabilities must lie between 0 and 1, and the joint probability cannot exceed P(B) (or P(A)), since the overlap of two events can never be larger than either event on its own.
If you also supply P(A), the tool returns the reverse conditional P(B|A) = P(A∩B) / P(A) and tests for independence. Two events are independent when knowing one tells you nothing about the other, which holds exactly when P(A∩B) = P(A)·P(B). The calculator compares the entered joint probability against that product (within a tiny numerical tolerance) and reports the events as independent or dependent.
The donut chart shows P(A∩B) as a slice of P(B), illustrating what fraction of outcomes in B also belong to A — that fraction is precisely P(A|B). Division by zero is guarded: if P(B) is 0 the conditional is undefined and no result is shown.
Frequently asked questions
Joint probability P(A∩B) is the chance both events happen together. Conditional probability P(A|B) is the chance A happens given B already occurred, found by dividing the joint probability by P(B).
Events A and B are independent when P(A∩B) = P(A)·P(B). Enter P(A) as well and the calculator checks this equality for you, labeling the events independent or dependent.
The overlap of A and B is a subset of B, so it can never be more probable than B itself. If you enter a joint probability larger than P(B), the inputs are inconsistent and no result is returned.
Also known as
TG we-Calculate Editorial Team. (2026). Conditional Probability Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/conditional-probability-calculator
TG we-Calculate Editorial Team. "Conditional Probability Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/conditional-probability-calculator.
TG we-Calculate Editorial Team, "Conditional Probability Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/conditional-probability-calculator
@misc{wecalculate_conditional_probability_calculator, title = {Conditional Probability Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/conditional-probability-calculator}}, year = {2026}, note = {TG we-Calculate} }
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